Continuity mistake: When the B2 releases the nuke it banks away to the left, however the next radar shot shows it flying away to the right.
Continuity mistake: When Will Smith and Jeff Goldblum are in the mothership, Will says that once the missile is fired they have 30 seconds to get out of the ship before it explodes. The sequence of events, portrayed in real-time, from the start of the countdown to the detonation is 93 seconds. By the time 30 seconds has elapsed; they are just barely getting to the inner-triangle opening, with 23 seconds remaining. From here, it takes an additional 40 seconds to traverse 'the triangle' and exit the ship; with another 10 seconds passing after clearing the doors. The timer now shows 10 seconds remaining. Basically (according to the countdown), the first 30 seconds were depicted as being only 7 having elapsed; and the 50 seconds after that being only 13. Everything was in real-time. (02:18:25)
Continuity mistake: During the First Lady's death scene, Connie is on the First Lady's left, when the President asks his daughter to go out in the hallway. But in the very next shot, Connie is on the other side of the bed standing right next to the little girl. (01:39:55)
Continuity mistake: Near the end of the film, when all the main characters pull up in a jeep to meet David and Steven who have just returned to earth, Jasmine leaps out first and is shown running alone toward them, yet Connie gets to the men first. This cannot be explained by Connie being faster than Jasmine as the distance is too short(the rest of the group stroll to the men in only seconds). Connie would have to run like the wind.
Revealing mistake: When the Welcome Wagon is being shot down you can see an explosion starting inside the last helicopter before it is even being hit.
Continuity mistake: Near the end of the film as the shields come down, the jets start firing missiles at the ship. There is a shot of Randy Quaid's son walking through the control room at Area 51. Notice in the background, the lights are blinking on and off. The alien ship hasn't fired it's main weapon yet. Once it does they show the lights flickering off and on in the control room. These scenes are several minutes apart.
Continuity mistake: When the aliens arrive in New York City and start to come over the city we see a man selling candy who turns around to see the spacecraft overhead. When the scene changes we see the another man turning around and colliding with a women, and the background sky has no spacecraft in it. (00:22:40)